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blog.sigfpe.com | ||
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math.andrej.com
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| | | | | [AI summary] The provided text is a collection of comments and discussions from a blog post about the concept of computable functions and their continuity, with a focus on type I and type II computability. The discussion touches on various topics, including the Church-Turing thesis, the role of higher-order functions like m and timeout in different models of computation, and the distinction between constructive and classical mathematics. The comments also explore the implications of different computational models, such as PCF, Turing machines, and Type II computation, and their relevance to real-world applications. The overall theme is the exploration of the boundaries and nuances of computability and continuity in mathematical and computational contexts. | |
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kuruczgy.com
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| | | | | [AI summary] The article explores the intersection of functional programming and logic through the lens of dependent types. It begins with foundational concepts like type constructors and inductive types, then delves into the Curry-Howard isomorphism, which links programs to mathematical proofs. The discussion covers how types represent propositions, functions as implications, and inductive types as proof strategies. Examples include defining logical relations like less than or equal to and equality, and demonstrating how to prove properties like universal quantification and mathematical identities. The article concludes with an overview of resources for further study in proof assistants like Coq and Idris, emphasizing the practical applications of dependent... | |
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micromath.wordpress.com
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| | | | | Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... | |
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jack-clark.net
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| | | Note: Import AI now publishes via Substack; read and subscribe here. Google makes progress on the self-teaching universal translator:...Universal Speech Models scale beyond 100 languages...Google has built a family of AI systems called Universal Speech Models (USMs). These models are designed to do speech recognition on more than 100+ languages. The main model is 2B... | ||
